July 10-11, 2025
Ruhr University Bochum

Organizers: Karin Baur, Markus Reineke

Speakers

The list of the conference speakers includes the following:

• Daniel Bissinger (Kiel)
• Giulia Iezzi  (Aachen)
• Dani Kaufman (Leipzig)
• Daisie Rock (Leuven)
• Sibylle Schroll  (Cologne)

Schedule

Registration

Late registration is still open via this form.

Conference Dinner

A conference dinner is set to take place on July 10 at 18:30 at Beckmanns Hof in the Botanical Garden directly south of the Ruhr University's campus.

Accommodation

We recommend the following accommodation options close to campus or the central station:

• B&B Bahnhof-Süd
• Hotel Claudius
• B&B Bochum City
• acora Bochum Living in the City
• Landesspracheninstitut Bochum

Talks

Daniel Bissinger
On uniform and homogeneous Steiner bundles and reflection functors

Uniformity and homogeneity are classical and well-studied properties of vector bundles on projective space $\mathbb{P}^n$. While every homogeneous bundle is necessarily uniform, the converse does not hold for n > 1, as first demonstrated by Elencwajg in 1979. More recently, Marchesi and Miró-Roig have shown that uniform but non-homogeneous bundles already appear within the special class of so-called Steiner bundles.

In this talk, we outline the connection between Steiner bundles on Grassmannians and certain full subcategories of representations of generalized Kronecker quivers. Using this correspondence, we then present alternative proofs of known results for Steiner bundles, and describe how homogeneous and uniform Steiner bundles on $\mathbb{P}^n$ can be studied using Auslander-Reiten theory, recent results on general subrepresentations, and reflection functors.
Some of the results presented are part of joint work with Rolf Farnsteiner.

Giulia Iezzi
Quiver Grassmannians for linear degenerations of Schubert varieties

Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. For instance, this method was used to study linear degenerations of flag varieties, obtaining characterisations of flatness, irreducibility and normality via rank tuples.
In this talk, we discuss a class of smooth and irreducible quiver Grassmannians. By choosing appropriate dimension vectors, these varieties can be exploited to realise smooth Schubert varieties or to desingularise non-smooth ones. Then, we build upon this construction and define linear degenerations of Schubert varieties, giving a combinatorial description of  the isomorphism classes of certain quiver representations.

Daisie Rock
Semi-discrete cluster categories

Building on Keller's work and the construction in BMRRT, we present a candidate for a semi-discrete cluster category. We first recall the original definition of thread quivers from Berg and van Roosmalen and then present a generalized definition that we will work with. Under reasonable assumptions, the category of finitely presented representations of a generalized thread quiver is hereditary. We add an additional assumption, called quasi-locally discrete, in order to construct our cluster category. This ongoing joint work with Charles Paquette and Emine Yıldırım, part of which is available in arXiv:2410.14656.

Dani Kaufman
Positivity and Noncommutative Cluster Algebras

Given G a real Lie group and Theta a subset of its restricted roots, Guichard and Wienhard gave a definition of a positive structure in G with respect to Theta and classified all pairs (G, Theta) which admit such a structure. This classification includes split real Lie groups, Hermitian Lie groups of tube type, the groups SO(p,q) and an exceptional series. Such a structure produces a semigroup of positive elements of G called the Theta positive semigroup, which recovers Lusztig’s totally positive semigroup in the split real case. In recent and ongoing work with Anna Wienhard, Zachary Greenberg, and Merik Niemeyer, we prove that these theta positive semigroups and associated positive configuration spaces of flags are parametrized by the Positive J-valued points of an appropriate Noncommutative Polygonal Cluster Algebra  and J a Euclidian Jordan algebra. These noncommutative cluster algebras are generalizations of the noncommutative surface type cluster algebras due to Berenstein and Retakh. They appear as deformations of Fock-Goncharov cluster algebras of type B_p and G_2 and involve a mix of commuting and non-commutating variables along with some strange surface-like combinatorics. In this talk I will try to give a birds-eye view of the theory of Theta positivity and how it leads to these new noncommutative cluster algebras and highlight some of their surprising properties. 

Sibylle Schroll
On algebras derived equivalent to skew-gentle algebras

For classes of finite dimensional algebras, closure under derived equivalence is a rare property. By the work of Schröer and Zimmermann, the class of gentle algebras is closed under derived equivalence. On the other hand, the class of the closely related skew-gentle algebras - which are skew-group algebras of gentle algebras - is not closed under derived equivalence. In this talk, we will introduce the new class of semi-gentle algebras. We will show that every skew-gentle algebra is semi-gentle and any semi-gentle algebra is derived equivalent to a skew-gentle algebra. This based on joint work with Severin Barmeier and Zhengfang Wang as well as joint work in progress with Severin Barmeier, Cheol-Hyun Cho, Kyoungmo Kim, Kyungmin Rho and Zhengfang Wang. 

Short Talks

Maximilian Kaipel
Mutating ordered τ-rigid modules

A mutation operation for τ-exceptional sequences of modules over any finite-dimensional algebra was recently introduced, generalising the mutation for exceptional sequences of modules over hereditary algebras. In this talk I will interpret this mutation in terms of TF-ordered τ-rigid modules, which are in bijection with τ-exceptional sequences. As an application I will show that the mutation is transitive for Nakayama algebras. This is joint work with Aslak Buan and Håvard Terland. 

Alexander Pütz
Quasi-projective varieties are Grassmannians for fully exact subcategories of quiver representations

Reineke and independent other authors proved that every projective variety arises as a quiver Grassmannian. We prove the claim in the title by restricting Reineke's isomorphism to Grassmannians for a fully exact subcategory.

Janina Letz
The Hochschild cohomology ring of monomial algebras

The Hochschild cohomology of an associative algebra, equipped with the cup product, is a graded-commutative algebra. For a monomial algebra, the Hochschild cohomology can be computed using the Bardzell resolution, which is a minimal resolution. I will give an explicit description of a diagonal map on the Bardzell resolution for any monomial algebra. This diagonal map gives an explicit description of the cup product on Hochschild cohomology. As an application, I give a proof that the cup product is zero in positive degrees for triangular monomial algebras. This is joint work with Dalia Artenstein, Amrei Oswald and Andrea Solotar.

Kyungmin Rho
Geometric Fukaya categories of surfaces and tame representation problems

We consider the Fukaya category of surfaces whose objects are immersed curves with local systems, providing a minimal model for the corresponding A_infinity-category. It provides an integrated perspective to the classical tame problems arising from representation theory and algebraic geometry, including derived categories of gentle algebras, vector bundles over singular curves, and Cohen-Macaulay modules over singular surfaces.

Sabino Di Trani
Regularity in Linear Degenerations of Flag Variety

In the talk I will present some results about  regularity properties of linear degenerations of flag varity. I will give a classification of the linear degenerations of (partial) flag varieties that are smooth. Moreover, under certain condition on the dimension vector, I will prove that flat degeneration are regular in codimension 2, generalizing a result of Cerulli Irelli, Feigin and Reineke for Feigin degenerations.

Pablo Zadinaisky
Pieri's rule for gl(infinity)